Both Mohamed and Magag had been moved out of London under control orders but were able to return under the new regime before going on to flee.

As a result, Mrs May is planning to reintroduce a form of the relocation power which will allow individuals to be moved to other parts of the town or city in which they live.

Other measures under consideration include restricting access to specific mosques or time spent in them.

They could also be a lengthening of overnight curfews and an increase in the amount of times subjects have to report to the police each day.

The family of Mohamed, who is suspected of having links with the Somali terror group Al-Shabaab, said over the weekend that the controls he had been under with a Tpim had been “more laid back”.

Any moves to restore a relocation power will cause tensions in the Coalition.

When Tpims were being drawn up in 2011 senior Lib Dem MP Tom Brake, said: "Relocation is a crunch issue for the Liberal Democrats. We fought hard to get it removed.”

Yvette Cooper, the shadow home secretary, said David Cameron should now take charge of the issue, adding: “Theresa May is belatedly trying to close the stable door that she herself threw open.

"She made it impossible to relocate terror suspects, no one else. And she can't just blame the Liberal Democrats. Tory Ministers and back benchers – including the Home Secretary – were all keen to downgrade control orders after the election, because they refused to face the realities of government or listen to security warnings.”

James Brokenshire, the security minister, said: "The previous government's Control Orders were not working. Their powers were being struck down in the courts and seven suspects absconded from them — six of whom were never caught.”